A semi-analytical mathematical model for the pressure transient analysis of multiple fractured horizontal well with secondary fractures

Over the recent years, several researchers have performed pressure transient analysis (PTA) of multi-fractured horizontal wells (MFHWs). However, most of these studies only considered hydraulic fractures (HFs), and the effect of secondary fractures (SFs) was ignored. To this end, in this study, a semi-analytical model is established based on the discrete coordinate method to examine the influence of SFs on the transient pressure characteristics of MFHWs. The mathematical model is solved using Laplace transform theory, source function theory, and superposition principle, and the actual pressure of the reservoir is obtained using the Stehfest numerical inversion algorithm. The efficacy of the model is verified through an industrial simulator (Ecrin-KAPPA). Further, sensitivity analysis is conducted to examine the impact of fracture parameters on the MFHW with and without SFs. The results indicate that the reservoir with SFs undergoes eight flow regimes in which the SF radial flow is a new flow process. The number of SFs mainly affects the SF radial flow regime and the bilinear flow regime, while the SF half-length also affects the first linear flow regime in addition to the above two regimes. The fracture conductivity mainly affects the SF radial flow regime, the bilinear flow regime, and the first linear flow regime. Overall, the proposed model facilitates accurate and effective analysis of the dynamics of unconventional multi-fractured reservoirs, and it can be potentially used to interpret the characteristics of actual reservoir pressures on site.